The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction
Pure and Applied Mathematics Journal
Volume 6, Issue 4, August 2017, Pages: 108-113
Received: May 6, 2017;
Accepted: Jun. 14, 2017;
Published: Jul. 18, 2017
Views 2942 Downloads 96
Mashadi, Analysis and Geometry Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Chitra Valentika, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Sri Gemawati, Analysis and Geometry Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Hasriati, Analysis and Geometry Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.
The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction, Pure and Applied Mathematics Journal.
Vol. 6, No. 4,
2017, pp. 108-113.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Ainul Wardiyah, Mashadi and Sri Gemawati, Relationship of Lemoine circle with a symmedian point, JP Journal Math. Sci., 17 (2) (2016), 23–33.
B. J. McCartin, Mysteries of the Equilateral Triangle, Hikari Ruse, 2010.
B. Grunbaum, Is Napoleon′s theorem really Napoleon′s theorem, The American Mathematical Monthly, 119 (2012), 495–501.
G. A. Venema, Exploring advanced euclidean geometry with Geometer′s Sketchpad, http://www.math.buffalostate.edu/giambrtm/MAT521/eeg.pdf, accessed 26 july 2016.
J. A. H. Abed, A proof of Napoleon's theorem, The General Science Journal, (2009), 1-4.
J. E. Wetzel, Converses of Napoleon′s theorem, The American Mathematical Monthly, 99 (1992), 339–351.
Mashadi, Buku Ajar Geometri, Pusbangdik Universitas Riau, Pekanbaru, 2012.
Mashadi, Geometri Lanjut, Pusbangdik Universitas Riau, Pekanbaru, 2015.
Mashadi, S. Gemawati, Hasriati and H. Herlinawati, Semi excircle of quadrilateral, JP Journal Math. Sci. 15 (1 & 2) (2015), 1-13.
Mashadi, S. Gemawati, Hasriati and P. Januarti, Some result on excircle of quadrilateral, JP Journal Math. Sci. 14 (1 & 2) (2015), 41-56.
Mashadi, Chitra Valentika and Sri Gemawati, International Journal of Theoritical and Applied Mathematics, 3 (2), (2017), 54 – 57.
M. Corral, Trigonometry, http://www.biomech.uottawa.ca/fran09/enseignement/notes/ trgbook.pdf, accessed 26 july 2016.
N. A. A. Jariah, Pembuktian teorema Napoleon dengan pendekatan trigonometri, http://www.academia.edu/12025134/_Isi_NOVIKA_ANDRIANI_AJ_06121008018, accessed 6 Oktober 2015.
P. Bredehoft, Special Cases of Napoleon Triangles, Master of Science, University of Central Missouri, 2014.
P. Lafleur, Napoleon’s Theorem, Expository paper, http://www.Scimath.unl.edu/MIM/files/MATEexamFiles, accessed 24 November 2015.
V. Georgiev and O. Mushkarov, Around Napoleon′s theorem, http://www.dynamat.v3d.sk/ uploaddf 20120221528150.pdf, accessed 24 july 2016.
Zukrianto, Mashadi and S Gemawati, A Nonconvex Quadrilateran and Semi-Gergonne Points on it: Some Results and Analysis, Fundamental Journal of Mathematics and Mathematical Sciences, 6 (2), (2016), 111-124.